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Math lesson plan · 9th grade (Year 10 in England) · 45 minutes

Solve factorised equations with the zero product property

Algebra

CCSS HSA.REI.B.4.BCCSS HSA.SSE.B.3.AEngland: GCSE Foundation Algebra

Objective and success criteria

Students will: Solve factorised equations with the zero product property.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: One-step equations

Leads to: the next skill in this area.

Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 5 min

  • Quick retrieval from earlier learning (One-step equations). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Solve: x/9 = 4 → x = 36Prompt: x is divided by 9. What undoes dividing?
  2. Solve: x/4 = 0 → x = 0Prompt: x is divided by 4. What undoes dividing?
  3. Solve: x/2 = 11 → x = 22Prompt: x is divided by 2. What undoes dividing?

Hook · 5 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Solve factorised equations with the zero product property. Read the success criteria together.

I do: model it · 10 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: Solve: (x − 8)(x − 7) = 0. Give both solutions, separated by a comma.
  • Step 1: x − 8 = 0 or x − 7 = 0
  • Step 2: x = 8 or x = 7
  • Answer: x = 7 or x = 8
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 10 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. Solve: (x + 1)(x − 5) = 0. Give both solutions, separated by a comma. → x = -1 or x = 5Prompt: If a product equals zero, at least one factor equals zero.
  2. Solve: (2x + 1)(x + 3) = 0. Give both solutions (fractions are fine), separated by a comma. → x = -3 or x = -0.5Prompt: Set each factor equal to zero.

You do: independent practice · 10 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 5 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Solve: (3x + 7)(x + 4) = 0. Give both solutions (fractions are fine), separated by a comma. → x = -4 or x = -2.33333333333Prompt: Set each factor equal to zero.
  2. Solve: x(x + 3)(x − 4) = 0. Give all three solutions, separated by commas. → x = -3 or x = 0 or x = 4Prompt: There are three factors, so there can be three solutions.

Watch out for

  • Doing an operation to one side of an equation but not the other.
  • Reading 3x as 3 + x, or thinking x always stands for one particular number.

Support and stretch

Support

  • Review first: One-step equations.
  • Use concrete materials: balance scales or a balance drawing.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-9.

Free lesson plan from eurekami.com/lesson-plan-builder

eurekami

Solve factorised equations with the zero product property

Name

Date

Score/ 8

  1. Question 1

    Solve: (2x + 1)(x + 6) = 0. Give both solutions (fractions are fine), separated by a comma.

    x =

  2. Question 2

    Solve: x(x + 5)(x − 2) = 0. Give all three solutions, separated by commas.

    x =

  3. Question 3

    Solve: (x − 2)(x − 1) = 0. Give both solutions, separated by a comma.

    x =

  4. Question 4

    Solve: (5x + 9)(x + 2) = 0. Give both solutions (fractions are fine), separated by a comma.

    x =

  5. Question 5

    Solve: x(x + 3)(x − 7) = 0. Give all three solutions, separated by commas.

    x =

  6. Question 6

    Solve: (x − 4)(x − 5) = 0. Give both solutions, separated by a comma.

    x =

  7. Question 7

    Solve: (5x − 9)(x − 4) = 0. Give both solutions (fractions are fine), separated by a comma.

    x =

  8. Question 8

    Solve: x(x + 7)(x − 2) = 0. Give all three solutions, separated by commas.

    x =

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Answer key: Solve factorised equations with the zero product property

  1. 1. x = -6 or x = -0.5

  2. 2. x = -5 or x = 0 or x = 2

  3. 3. x = 1 or x = 2

  4. 4. x = -2 or x = -1.8

  5. 5. x = -3 or x = 0 or x = 7

  6. 6. x = 4 or x = 5

  7. 7. x = 1.8 or x = 4

  8. 8. x = -7 or x = 0 or x = 2